A note on the finite fractal dimension of the global attractors for dissipative nonlinear Schrödinger‐type equations

In this article, we present, throughout two basic models of damped nonlinear Schrödinger (NLS)–type equations, a new idea to bound from above the fractal dimension of the global attractors for NLS‐type equations. This could answer the following open issue: consider, for instance, the classical one‐dimensional cubic nonlinear Schrödinger equation $$u_t+i{u}_{xx}+i|u{|}^{2}u+\gamma u=f,f\in {\mathrm{??}}^2(?).$$ “How can we bound the fractal dimension of the associate global attractor without the need to assume that the external forcing term f has some decay at infinity (that is belonging to some weighted Lebesgue space)?”     

Substituent effects on the ring‐opening mechanism of gem‐dibromospiropentanes to related allenes: a theoretical study

Density functional theory computations at B3LYP and X3LYP levels were performed for ring openings of substituted gem‐dibromospiropentanes (R = ―H, ―Cl, ―Br, ―CH₃, ―SiH₃, ―OH, ―OCH₃, ―CF₃, ―BF₂, and ―SH) to related allenes. The conversion of spiropentanoids 5a , 5b , 5c , 5d , 5e , 5f , 5g , 5h , 5i , 5j to the corresponding allenes 7a , 7b , 7c , 7d , 7e , 7f , 7g , 7h , 7i , 7j can proceed in both concerted and stepwise mechanism except for R = ―H. Both ring‐opening mechanisms have similar activation energy barriers to open the spiropentanylidene ring and generate the structure of allene at all theoretical levels used herein. Generally the π electron‐donating group (―OH or ―SH) decreases the activation barrier for the follow‐up reaction of 1‐bromo‐1‐lithiospiropentanoid and free spiropentanylidene. Hence, both bearing electron‐donating substituents are more reactive than those with electron‐withdrawing group, and the first one to open the ring to the LiBr–allene complex does so more readily than the second. The sEDA index used to measure sigma‐electron excess/deficiency of the cyclopropylidene ring is mutually correlated for the studied systems. Copyright © 2015 John Wiley & Sons, Ltd.     

Stepanov ergodic perturbations for some neutral partial functional differential equations

In this work, we give sufficient conditions for the existence and uniqueness of μ?pseudo almost periodic integral solutions for some neutral partial functional differential equations with Stepanov μ?pseudo almost periodic forcing functions. Our working tools are based on the variation of constant formula and the spectral decomposition of the phase space. To illustrate our main results, we give applications to a neutral model arising in physical systems, as well as an application to heat equations with discrete and continuous delay. Copyright © 2015 John Wiley & Sons, Ltd.     

Renal-related perinephric fluid collections: MRI findings

We retrospectively reviewed MR studies on 10 patients with renal-related perinephric fluid collections who underwent MRI in three institutions between January 2001 and August 2004. All patients underwent MRI of the abdomen and T1-weighted, T2-weighted and serial contrast-enhanced images, including delayed-phase contrast-enhanced images 10-12 min after contrast injection, were obtained. Perinephric fluid collections in 5 patients revealed MRI findings of simple fluid content (i.e., hypointense on T1-weighted images and hyperintense on T2-weighted images). In another 5 patients, a complex perinephric fluid content (i.e., mixed hyper/hypointense on T1-weighted images and mixed hypo/hyperintense on T2-weighted images compatible with blood breakdown products and pus) was observed. In 5 patients, contrast extravasation on late-phase images that was compatible with urine leak was demonstrated. Our results suggest that MRI may determine the content of perinephric fluid collections on noncontrast T1-weighted and T2-weighted images and that contrast extravasation on late-phase images is associated with urine extravasation from renal collecting systems.     

Homogenization of a three-phase flow model in porous media

We give homogenization results for an immiscible and incompressible three-phase flow model in a heterogeneous petroleum reservoir with periodic structure, including capillary effects. We consider a model which leads to a coupled system of partial differential equations which includes an elliptic equation and two nonlinear degenerate parabolic equations of convection–diffusion types. Using two-scale convergence, we get an homogenized model which governs the global behavior of the flow. The determination of effective properties require the numerical resolution of local problems in a standard cell.     

Redox equilibria of iron oxides in aqueous-based magnetite dispersions: effect of pH and redox potential

The effect of pH and redox potential on the redox equilibria of iron oxides in aqueous-based magnetite dispersions was investigated. The ionic activities of each dissolved iron species in equilibrium with magnetite nanoparticles were determined and contoured within the Eh-pH framework of a composite stability diagram. Both standard redox potentials and equilibrium constants for all major iron oxide redox equilibria in magnetite dispersions were found to differ from values reported for noncolloidal systems. The "triple point" position of redox equilibrium among Fe(II) ions, magnetite, and hematite shifted to a higher standard redox potential and an equilibrium constant which was several orders of magnitude higher. The predominant area of magnetite stability was enlarged to cover a wider range of both pH and redox potentials as compared to that of a noncolloidal magnetite system.     

Immersed boundary method for unsteady kinetic model equations

Predicting unsteady flows and aerodynamic forces for large displacement motion of microstructures requires transient solution of Boltzmann equation with moving boundaries. For the inclusion of moving complex boundaries for these problems, three immersed boundary method flux formulations (interpolation, relaxation, and interrelaxation) are presented. These formulations are implemented in a 2‐D finite volume method solver for ellipsoidal‐statistical (ES)‐Bhatnagar‐Gross‐Krook (BGK) equations using unstructured meshes. For the verification, a transient analytical solution for free molecular 1‐D flow is derived, and results are compared with the immersed boundary (IB)‐ES‐BGK methods. In 2‐D, methods are verified with the conformal, non‐moving finite volume method, and it is shown that the interrelaxation flux formulation gives an error less than the interpolation and relaxation methods for a given mesh size. Furthermore, formulations applied to a thermally induced flow for a heated beam near a cold substrate show that interrelaxation formulation gives more accurate solution in terms of heat flux. As a 2‐D unsteady application, IB/ES‐BGK methods are used to determine flow properties and damping forces for impulsive motion of microbeam due to high inertial forces. IB/ES‐BGK methods are compared with Navier–Stokes solution at low Knudsen numbers, and it is shown that velocity slip in the transitional rarefied regime reduces the unsteady damping force. Copyright © 2015 John Wiley & Sons, Ltd.     

Photothermal heterodyne imaging of individual nonfluorescent nanoclusters and nanocrystals

We introduce a new, highly sensitive, and simple heterodyne optical method for imaging individual nonfluorescent nanoclusters and nanocrystals. A 2 order of magnitude improvement of the signal is achieved compared to previous methods. This allows for the unprecedented detection of individual small absorptive objects such as metallic clusters (of 67 atoms) or nonluminescent semiconductor nanocrystals. The measured signals are in agreement with a calculation based on the scattering field theory from a photothermal-induced modulated index of refraction profile around the nanoparticle.     

Dissolution kinetics of fluorapatite in the hydrochloric acid solution

A thermochemical study of hydrochloric acid attack of synthetic fluorapatite was performed by a DRC. The calculated thermogenesis curves show one peak. The plot of the heat quantity as a function of the dissolved mass undergoes only one straight segment, and the thermogenesis curves present a single peak, suggesting the occurrence of a one-step dissolution process. The dissolution kinetics was examined according to the heterogeneous reaction models and showed that the dissolution is controlled by the product layer diffusion process with a reaction rate expressed by the following semiempirical equation; \(\left[ {1 + 2(1 - X) - 3(1 - X)^{{\frac{2}{3}}} } \right] = 3195 \times 10^{ - 2} C^{0.145} \left( {\frac{S}{L}} \right)^{ - 0.628} e^{{ - \frac{2600}{\text T}}} t\). The activation energy was determined as 21.6 ± 1.5 kJ mol^?1